Story in a movie.
Before we continue think about where games show you the story. Identify the places and write them down.
Like mentioned the story can't be forced. We need to place it to places where player will most likely get at least something of it and a bit all around.
Here places where you'll find story:
Very often I see a story added to the game. But the story describes events that happen before the game, not during the game. To make the story and game work together, make the story events happen during the game! Make the game trigger the events in the game!
Could Tetris have a story? Yes, it could. The story could be about building a city, a forest or even robots or cars. The theme and setting will affect the story and the other way around.
The story needs progress during the game, not happen before the game.
Where will the story be told? Probably for Tetris in the popups before a game starts, in loading screens, in the level objectives and score cards.